I don't quite note how it would all go away with less full buses passing more full buses.
For one thing, it would be incorrect for an empty bus to pass a full bus - a full bus can't take any more passengers, and the people who don't fit on the full bus would have to wait even longer, for the next bus again.
Secondly, people get off at stops, not just get on. The bus that overtakes won't get a big lead, because it probably has to stop anyway. It can only leave when it looks like the front bus is going to fit all the passengers.
Thirdly, the bunching that has already occurred (to make it possible for one bus to overtake another) means that the bus stops ahead have far more people at them. Instead of merely bunching together, one full bus followed by one empty bus, you'd have two fairly full buses leap-frogging one another.
The only way get back to a situation where the buses are on opposite sides again, minimizing variance in bus wait time, is to have a bus pause when it gets too far ahead of schedule.
Note that bunching isn't actually the problem—in fact, bus runs are frequently planned in bunches, with two shorter busses arriving in series simulating a the arrival of a single double-length bus.
The problem, in practice, is people cramming into the nearly-full first bus of a bunch (and delaying the bus further as people slowly fight their way off and on), with another nearly-empty bus following along with nobody getting on it.
This problem would go away if people could be trained to wait for the second bus in the "bunch", rather than getting on the lead one. But, since that change-of-perspective is unlikely to happen, "two fairly full busses leap-frogging one-another" is actually a good solution. It's load-balancing, basically.
For bus stops with live status displays, this is reasonable. In cities where there's no indication of when the next bus is, there's no live-monitoring facility available on the phone, and the driver's response to "when is the next bus?" is "dunno"—you can bet I'll cram on that bus.
Why are buses planned to arrive in bunches? Double-length buses save a driver, but if you have two single-length buses, what's the advantage to bunching?
it would be incorrect for an empty bus to pass a full bus
You've got it precisely backwards.
If the empty bus passes the full bus, then the empty bus is picking up passengers, while the full bus, arriving at freshly cleared stops, only unloads.
Eventually the loading factor levels out and the problem's cleared
Indeed, so the empty bus will slow down and the full bus will speed up a little (as it still has to drop off passengers), and they will meet and switch places again; so the two buses will start leap-frogging each other all the time, as GP described. So they will tend to stay together, and not spread out as desired.
That's even worse. They will just keep together, and the bus at the back (which was the initial full bus) will have to wait for the bus at the front without any good reason.
No, that's exactly what you're trying to accomplish.
You're already got a headway interruption. Both buses are arriving at stops after a longer-than-usual interval. That means there are more passengers waiting.
You've put the empty bus ahead of the full one. It picks up the waiting passengers.
The full bus trails, briefly, it discharges passengers, but loads none (or at worst, a very few).
This continues either to the end of the line (at which point regular headways are once again established), or, possibly, until the lead bus becomes full. At that point, you might swap positions, but only then.
If you were to put the full bus in the lead because it was "getting delayed", you'd only re-create the problem you initially had: of a full bus trying to load and unload passengers, which happens much more slowly than for an empty bus, while the less loaded bus that can accomplish loadings/unloadings faster trails behind.
Your letting the trailing, full bus lead doesn't save time.
Well, I guess you can't make it much better than your method anyway, and it does have the advantage that people will see both buses arrive at nearly the same time, so there's that.
For one thing, it would be incorrect for an empty bus to pass a full bus - a full bus can't take any more passengers, and the people who don't fit on the full bus would have to wait even longer, for the next bus again.
Secondly, people get off at stops, not just get on. The bus that overtakes won't get a big lead, because it probably has to stop anyway. It can only leave when it looks like the front bus is going to fit all the passengers.
Thirdly, the bunching that has already occurred (to make it possible for one bus to overtake another) means that the bus stops ahead have far more people at them. Instead of merely bunching together, one full bus followed by one empty bus, you'd have two fairly full buses leap-frogging one another.
The only way get back to a situation where the buses are on opposite sides again, minimizing variance in bus wait time, is to have a bus pause when it gets too far ahead of schedule.